Abstract
In this chapter, we discuss the basic properties of Laplace functionals of random measures, which provide an important tool in the study of measure-valued processes. In particular, we give some characterizations of the convergence of random measures in terms of their Laplace functionals. Based on these results, a general representation for the distributions of infinitely divisible random measures is established. We also give some characterizations of continuous functions on the positive half line with Lévy–Khintchine type representations.
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© 2011 Springer-Verlag Berlin Heidelberg
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Li, Z. (2011). Random Measures on Metric Spaces. In: Measure-Valued Branching Markov Processes. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15004-3_1
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DOI: https://doi.org/10.1007/978-3-642-15004-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15003-6
Online ISBN: 978-3-642-15004-3
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